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Keywords:
convective heat-transport; two-point convection-diffusion boundary-value problem; optimization of the amount of heat
Summary:
The one-dimensional steady-state convection-diffusion problem for the unknown temperature \$y(x)\$ of a medium entering the interval \$(a,b)\$ with the temperature \$y_{\min }\$ and flowing with a positive velocity \$v(x)\$ is studied. The medium is being heated with an intensity corresponding to \$y_{\max }-y(x)\$ for a constant \$y_{\max }>y_{\min }\$. We are looking for a velocity \$v(x)\$ with a given average such that the outflow temperature \$y(b)\$ is maximal and discuss the influence of the boundary condition at the point \$b\$ on the “maximizing” function \$v(x)\$.
References:
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[3] Kamke, E.: Handbook on Ordinary Differential Equations. Nauka, Moscow, 1971, (in Russian).
[4] Roos, H.-G., Stynes, M., Tobiska, L.: Numerical Methods for Singularly Perturbed Differential Equations. Springer, Berlin, 1996. MR 1477665 | Zbl 0844.65075

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